I don't know if it's possible to get data on this, but I can't believe this happens more than once a month - and that seems generous.
- It's very quick to add a bounty. It's not like writing an answer where you worry about spacing and code formatting and getting all your links right. It's s 15 second operation AT MOST
- It's unlikely that two users will want to bounty the same question at the same time in the first place
So, to pay off, we need to have a high frequency of multiple users posting bounties in the same 15-second window on the same question.
And the big problem that we would avoid by adding a special trap for this extremely rare scenario is...minor inconvenience and possible confusion? It should be pretty obvious what has happened if you do this, as you yourself mention in the comments.
You say "itd confuse some people" but we are talking about 1 additional confused person a month, which for SO is like a single hydrogen atom somewhere in the vastness of the sun.
Even if it only took 15 minutes of admin time to put this in place, it'll take 5 years (assuming 1 occurrence a month that costs someone 15 seconds) for it to pay off. In 5 years we will all be answering questions with our minds anyways so it will be a moot point.